Apple(and Google) has unique advantages as the owners of the major platforms, and and major mapping apps, with access to all travel data. Those are major building blocks of such a travel service.

Mapping data isn't travel data. One is useful for representing the world, the other is only useful for marketing data.

What access does Apple have to travel data?

It has access to all the location data of each of it's users.

Except that they've made a big deal lately of differentiating themselves from Google by not using your data.

That's what I thought, unsure if it's true. But Tim Cook was making a big deal about the lack of data collection.